Question

The radius of a sphere is increasing at a rate of 4 mm/s. How fast is the volume increasing when the diameter is 60 mm?

Answer 1

you are told the radius is increasing at a rate of 4mm/s

this tells us that
dr/dt=4mm/s


you want to find
dv/dt

you are given diameter=60mm


so you want to find
dv/dt=
to get this

dv/dt=dv/dr x dr/dt

Answer 2

dv/dt = 3r x dr/dt

Answer 3

r = radius = diameter / 2

Answer 4

V = 4/3 x pi x r^3
differentiate with respect to time
dV/dt = 3r x dr/dt

Answer 5

Did you understand it now?